A First Course In Mathematical Logic And Set Theory

Author: Michael L. O'Leary
Publisher: John Wiley & Sons
ISBN: 0470905883
Size: 18.11 MB
Format: PDF, Kindle
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Rather than teach mathematics and the structure of proofssimultaneously, this book first introduces logic as the foundationof proofs and then demonstrates how logic applies to mathematicaltopics. This method ensures that readers gain a firmunderstanding of how logic interacts with mathematics and empowersthem to solve more complex problems. The study of logic andapplications is used throughout to prepare readers for further workin proof writing. Readers are first introduced tomathematical proof-writing, and then the book provides anoverview of symbolic logic that includes two-column logicproofs. Readers are then transitioned to set theory andinduction, and applications of number theory, relations, functions,groups, and topology are provided to further aid incomprehension. Topical coverage includes propositional logic,predicate logic, set theory, mathematical induction, number theory,relations, functions, group theory, and topology.

Set Theory

Author: Daniel W. Cunningham
Publisher: Cambridge University Press
ISBN: 1316682048
Size: 66.93 MB
Format: PDF, Mobi
View: 7363

Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.

Introduction To Mathematical Logic Fourth Edition

Author: Elliott Mendelson
Publisher: CRC Press
ISBN: 9780412808302
Size: 77.45 MB
Format: PDF
View: 7624

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

First Course In Mathematical Logic

Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 0486150941
Size: 14.66 MB
Format: PDF, ePub
View: 1954

Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.

Naive Mengenlehre

Author: Paul R. Halmos
Publisher: Vandenhoeck & Ruprecht
ISBN: 9783525405277
Size: 33.92 MB
Format: PDF, ePub, Docs
View: 6083

Satan Cantor Und Die Unendlichkeit

Author: Raymond Smullyan
Publisher: Springer-Verlag
ISBN: 3034862318
Size: 32.65 MB
Format: PDF, ePub
View: 6413

A Course On Mathematical Logic

Author: Shashi Mohan Srivastava
Publisher: Springer Science & Business Media
ISBN: 1461457467
Size: 42.92 MB
Format: PDF
View: 902

This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.

Principia Mathematica

Publisher:
ISBN:
Size: 21.77 MB
Format: PDF, ePub, Docs
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Proofs And Fundamentals

Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
ISBN: 9781441971272
Size: 45.17 MB
Format: PDF, ePub, Mobi
View: 7259